# morphsnakes

**Repository Path**: mirrors_lepy/morphsnakes

## Basic Information

- **Project Name**: morphsnakes
- **Description**: Morphological snakes for image segmentation and tracking
- **Primary Language**: Unknown
- **License**: BSD-3-Clause
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2020-09-25
- **Last Updated**: 2025-07-26

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README


====================
Morphological Snakes
====================

The *Morphological Snakes* are a family of related methods for image-guided
evolution of curves and surfaces represented as a level-set of an embedding
function. They have application in several computer vision areas, such as
tracking and image segmentation.

The first ideas of *Morphological Snakes* were introduced in [2]_. [1]_
completes that work describing the underlying mathematical foundations,
extending the application to the two-dimensional and three-dimensional cases,
and introducing two new algorithms: *Morphological Geodesic Active Contours* and
*Morphological Active Contours Without Edges*.

Background
==========

The contour evolution methods have been known in the Computer Vision community
for years, perhaps being the *Geodesic Active Contours* and the *Active Contours
without edges* the two most prominent examples. They both try to find a contour
that serves as a boundary to separate the image in two areas (usually called
*foreground* and *background*) based on the contents of the image. Both methods
work by solving partial differential equations (PDEs) on an embedding function
that has the contour as its zero-levelset.

The morphological snakes aim to provide a very fast, simple and stable
approximation to the solution of these PDEs. They do so substituting the terms
of the PDE by the repeated application of morphological operators over a binary
embedding function.

The *morphological operators* are defined as translation and contrast-invariant
operators. A morphological operator transforms an input function depending only
on the shape of its levelsets. For example, two very well known morphological
operators are the *dilation* and the *erosion*.

Brief theoretical description
=============================

The PDE for the Geodesic Active Contours (GAC) is

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/eq1.png

This PDE is the sum of three terms. From left to right, the smoothing term, the
balloon term and the image attachment term. It is well-known that the balloon
term can be solved by the repeated application of a dilation (or erosion)
operator with a small radius. Similarly, it is easy to simulate the image
attachment term with simple binary rules. However, it is not so easy for the
smoothing term.

[1]_ introduces a new morphological operator, the *curvature operator*, and
proves that it is a very good approximation to the mean curvature flow given by
the smoothing term. With this new operator, [1]_ also introduces the
*Morphological Geodesic Active Contours* (MorphGAC).

The MorphGAC consists of the approximation to the above PDE of the GAC with
the composition of the dilation, the erosion and the curvature operator. 

In a very similar way, the Active Contours without Edges (ACWE) evolves the
embedding function using the PDE

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/eq2.png

[1]_ describes the Morphological ACWE (MorphACWE) approximating this PDE with
the dilation, the erosion and the curvature operator.

Examples
========

The images below show some working examples of the Morphological Snakes.

MorphGAC
--------

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/nodule.gif

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/starfish.gif

MorphACWE
---------

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/lakes.gif

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/europe.gif

.. image:: https://raw.github.com/pmneila/morphsnakes/master/examples/dendrite.gif

Implementation
==============

The code provided is a Python implementation of the Morphological Snakes
methods. It does not aim to be a fast or efficient implementation. Instead, it
is intended to be as brief, understandable and self-contained as possible.

The code is documented and in ``tests.py`` there are some usage examples.

References
==========

.. [1] *A morphological approach to curvature-based evolution
   of curves and surfaces*. Pablo Márquez-Neila, Luis Baumela, Luis Álvarez.
   In IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI).

.. [2] *Morphological Snakes*. Luis Álvarez, Luis Baumela, Pablo Márquez-Neila.
   In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 2010 (CVPR10).

.. |figurespath| replace:: .